Universal Gravitation Study Pack
Kibin's free study pack on Universal Gravitation includes a 6-section study guide, 25 quiz questions, 30 flashcards, and 5 open-ended Explain review questions. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.
Last updated May 27, 2026
Universal Gravitation Study Guide
Master Newton's Law of Universal Gravitation — from the F = G(m₁m₂)/r² formula and the inverse-square relationship to surface gravity, orbital motion, and how one law unifies falling objects with planetary orbits.
Key Takeaways
- •Newton's Law of Universal Gravitation states that every pair of masses attracts each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
- •The gravitational force is calculated as F = G(m₁m₂)/r², where G is the universal gravitational constant, approximately 6.674 × 10⁻¹¹ N·m²/kg².
- •Doubling the distance between two objects reduces the gravitational force to one-quarter of its original value, a consequence of the inverse-square relationship.
- •Surface gravity on any planet or moon depends on that body's mass and radius, explaining why gravitational acceleration differs across planets even though G is universal.
- •Newton unified terrestrial and celestial mechanics by showing that the same gravitational law governing falling apples also governs the orbits of moons and planets.
- •Gravitational force is always attractive, acts along the line connecting the two centers of mass, and has infinite range, though it weakens with distance.
- •Orbital motion results from gravitational force providing the centripetal acceleration needed to keep a satellite on a curved path rather than traveling in a straight line.
The Core Law: Force Between Any Two Masses
Newton's Law of Universal Gravitation provides a precise mathematical description of the attractive force that exists between any two objects with mass, regardless of their composition or location in the universe.
Statement of the Law
- •Every mass in the universe exerts an attractive gravitational force on every other mass.
- •The magnitude of this force is directly proportional to the product of the two masses (m₁ and m₂) and inversely proportional to the square of the center-to-center distance (r) between them.
- •The relationship is expressed as F = G(m₁m₂)/r², where F is the gravitational force in newtons.
The Universal Gravitational Constant G
- •G has a measured value of approximately 6.674 × 10⁻¹¹ N·m²/kg², a constant that appears the same everywhere in the universe.
- •Because G is extremely small, gravitational forces between everyday objects (two people, two cars) are negligibly weak; only when at least one object is astronomically massive does gravity become significant.
- •Henry Cavendish first measured G experimentally in 1798 using a torsion balance apparatus that detected the tiny gravitational attraction between lead spheres.
Newton's Third Law and Gravitational Pairs
- •Gravity obeys Newton's Third Law: if Earth pulls you downward with a certain force, you pull Earth upward with an equal and opposite force.
- •The forces in a gravitational pair are equal in magnitude but produce vastly different accelerations because Earth's mass is enormous compared to a person's mass.
The Inverse-Square Relationship and Distance Effects
The inverse-square nature of gravitation is one of its most important mathematical properties, governing how rapidly gravitational force weakens as objects move apart.
How Force Changes with Distance
- •Because force depends on 1/r², doubling the distance reduces the gravitational force to (1/2)² = 1/4 of its original value.
- •Tripling the distance reduces the force to 1/9; increasing distance by a factor of 10 reduces force to 1/100.
- •Gravitational force never reaches exactly zero — it decreases continuously but extends to infinite range.
Measuring Distance: Center-to-Center, Not Surface-to-Surface
- •The variable r in the gravitational formula represents the distance between the centers of mass of the two objects, not between their surfaces.
- •For a person standing on Earth's surface, r equals Earth's radius (approximately 6.371 × 10⁶ m), not zero.
- •This center-to-center convention is valid for spherically symmetric objects, where all mass can be treated as concentrated at the geometric center.
Surface Gravity and the Acceleration Due to Gravity
Although G is universal, the gravitational acceleration experienced at the surface of a planet or moon varies depending on that body's specific mass and radius.
Deriving Gravitational Acceleration at a Surface
- •Setting the gravitational force equal to ma (Newton's Second Law) for an object of mass m on a planet of mass M and radius R gives: g = GM/R².
- •The object's own mass cancels out, which is why all objects fall with the same gravitational acceleration at a given location, regardless of how heavy they are.
- •Earth's surface gravitational acceleration is approximately 9.8 m/s², derived directly from Earth's mass (5.97 × 10²⁴ kg) and radius.
Comparing Surface Gravity Across Bodies
- •The Moon has about 1/6 of Earth's surface gravity because, despite having much less mass, its smaller radius partially compensates — but the mass difference dominates.
- •Jupiter's surface gravity is roughly 2.5 times Earth's because its enormous mass (318 times Earth's) far outweighs the effect of its larger radius.
- •A planet could theoretically have the same surface gravity as Earth if it had a different combination of mass and radius that produces the same GM/R² ratio.
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Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.
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What is the value of the universal gravitational constant G?
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Newton's Law of Universal Gravitation
Explain Newton's Law of Universal Gravitation in your own words. What does the formula F = G(m₁m₂)/r² tell us, and what makes this law 'universal'?
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